Scalene Triangle

A scalene triangle is a type of triangle in which all three sides have different lengths. This means that none of the three angles in a scalene triangle are equal to each other.

Properties of a Scalene Triangle:

• Three sides of different lengths
• Three interior angles of different measures
• No lines of symmetry
• Area can be calculated using Heron's formula:
  A = √(s(s-a)(s-b)(s-c))
  where a, b, and c are the side lengths, and s is the semi-perimeter of the triangle (s = (a+b+c)/2)

Example:

Consider a triangle with side lengths of 5 cm, 7 cm, and 9 cm. This triangle is a scalene triangle because all three sides have different lengths. The three angles of this triangle will also be different from each other.

Study Guide:

To identify a scalene triangle, remember the following key points:

• All three sides of different lengths
• No angles of equal measures
• No lines of symmetry

Practice problems:

1. Identify whether the following triangles are scalene or not:
1. Side lengths: 3 cm, 4 cm, 5 cm
2. Side lengths: 6 cm, 6 cm, 8 cm
3. Side lengths: 7 cm, 10 cm, 12 cm
2. Calculate the area of the following scalene triangles:
1. Side lengths: 5 cm, 8 cm, 10 cm
2. Side lengths: 9 cm, 12 cm, 15 cm